Theorem REF  is novel to the best of
our knowledge even though we use standard tools and techniques for
proving it. We first connect upper bounds of the metric entropy of
\(\mathcal {D}_m\)  to lower bounds of the small ball probability of
integrated Brownian sheet based on the ideas from [1]} and [2]} and the
results from [3]} and [4]}. The small ball probability of integrated Brownian
sheet here refers to the quantity
\(\mathbb {P}\Big (\sup _{t \in [0, 1]^m} |X_m(t)| \le \epsilon \Big ),\) 
